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Gradients and areas under graphs: OCR GCSE Maths questions

Every OCR GCSE Maths exam question on A15 Gradients and areas under graphs, 2017–2025, with its mark scheme and examiner’s report.

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921 questions

  1. Q20

    June 2025 · Paper 6

    5 marksA15 Gradients and areas under graphsR11 Compound units: speed, density and pressure
    The whole paper ↗
    June 2025 Paper 6, question 20: A container takes 8 minutes to be filled with water. The graph shows the rate of flow, in litres per minute, of the water into the container during the 8 minute

  2. Q19

    November 2024 · Paper 6

    6 marksR15 Instantaneous and average rates of changeA15 Gradients and areas under graphs
    The whole paper ↗
    November 2024 Paper 6, question 19: This graph shows the depth of the water, in centimetres, at a particular point in a river over a period of 10 hours. 40 30 Depth of the water 20 (cm) 10 9.00 10

  3. Q18

    June 2024 · Paper 4

    9 marksA15 Gradients and areas under graphsA14 Graphs in real contexts
    The whole paper ↗
    June 2024 Paper 4, question 18: (a) The graph shows the speed of an object during the first 20 seconds of its motion. 15 10 Speed (m/s) 5 0 5 10 15 20 Time (s) Calculate the distance travelled

  4. Q19

    June 2023 · Paper 4

    5 marksA15 Gradients and areas under graphsA14 Graphs in real contexts
    The whole paper ↗
    June 2023 Paper 4, question 19: The graph shows the velocity of a particle over the first 20 minutes of its motion. Velocity Not to scale (m / min) v 0 0 7 15 20 Time (mins) Between 7 minutes

  5. Q16

    November 2022 · Paper 5

    4 marksA15 Gradients and areas under graphsR15 Instantaneous and average rates of change
    The whole paper ↗
    November 2022 Paper 5, question 16: The graph shows the distance travelled by a particle over the first 20 seconds of its motion. 40 35 30 25 Distance 20 (metres) 15 10 5 0 0 5 10 15 20 Time (seco

  6. Q12

    November 2022 · Paper 6

    6 marksA15 Gradients and areas under graphsR14 Gradient as a rate of change
    The whole paper ↗
    November 2022 Paper 6, question 12: The graph shows the speed of a car during the first 40 seconds of a journey. 20 15 Speed 10 (m/s) 5 0 0 5 10 15 20 25 30 35 40 Time (s) (a) Write down the accel

  7. Q12

    June 2022 · Paper 5

    6 marksA15 Gradients and areas under graphsA14 Graphs in real contexts
    The whole paper ↗
    June 2022 Paper 5, question 12: An athlete goes for a training run. The graph shows their speed as they run. 4 Not to scale Speed (m/s) 0 400 1000 1200 Time (secs) (a) Write down the athlete’s

  8. Q19

    November 2020 · Paper 4

    9 marksA15 Gradients and areas under graphsR15 Instantaneous and average rates of change
    The whole paper ↗
    November 2020 Paper 4, question 19: (a) The graph shows the speed of a vehicle during the first 40 seconds of motion. 40 35 30 25 Speed 20 (m / s) 15 10 5 0 0 5 10 15 20 25 30 35 40 Time (s) Calcu

  9. Q19

    November 2019 · Paper 4

    4 marksA15 Gradients and areas under graphsR15 Instantaneous and average rates of change
    The whole paper ↗
    November 2019 Paper 4, question 19: The graph shows the distance travelled by a particle over 8 seconds. 12 11 10 9 8 7 Distance (metres) 6 5 4 3 2 1 0 0 1 2 3 4 5 6 7 8 Time (seconds) Estimate th

  10. Q14

    June 2019 · Paper 4

    7 marksA14 Graphs in real contextsA15 Gradients and areas under graphs
    The whole paper ↗
    June 2019 Paper 4, question 14: The graph shows the speed of a train during the first 60 seconds of motion. 25 20 15 Speed (m / s) 10 5 0 0 5 10 15 20 25 30 35 40 45 50 55 60 Time (s) (a) What

  11. Q8

    November 2018 · Paper 6

    7 marksA15 Gradients and areas under graphsR14 Gradient as a rate of change
    The whole paper ↗
    November 2018 Paper 6, question 8: The graph shows the speed of a cyclist during 20 seconds of a journey. 14 12 10 8 Speed (m/s) 6 4 2 0 2 4 6 8 10 12 14 16 18 20 Time (s) (a) Find the accelerati

  12. Q8

    June 2018 · Paper 6

    9 marksA15 Gradients and areas under graphsR1 Converting units
    The whole paper ↗
    June 2018 Paper 6, question 8: The graph shows the speed of a tram as it travels from the library to the town hall. Speed Not to scale (m/s) 6 0 65 85 Time (s) (a) Calculate the deceleration

  13. Q13

    November 2017 · Paper 5

    10 marksA15 Gradients and areas under graphs
    The whole paper ↗
    November 2017 Paper 5, question 13: The graph shows information about the speed of a vehicle during the final 50 seconds of a journey. At the start of the 50 seconds the speed is k metres per seco

  14. Q20

    June 2017 · Paper 4

    2 marksA15 Gradients and areas under graphs
    The whole paper ↗
    June 2017 Paper 4, question 20: The graph shows the speed, in metres per second, of a particle over the first four seconds of motion. 16 15 14 13 12 11 10 9 Speed (m/s) 8 7 6 5 4 3 2 1 0 0 1 2
All 14 questions on Gradients and areas under graphs, as a list
  1. June 2025, Paper 6, Q20 (5 marks): A container takes 8 minutes to be filled with water. The graph shows the rate of flow, in litres per minute, of the water into the container during the 8 minute
  2. November 2024, Paper 6, Q19 (6 marks): This graph shows the depth of the water, in centimetres, at a particular point in a river over a period of 10 hours. 40 30 Depth of the water 20 (cm) 10 9.00 10
  3. June 2024, Paper 4, Q18 (9 marks): (a) The graph shows the speed of an object during the first 20 seconds of its motion. 15 10 Speed (m/s) 5 0 5 10 15 20 Time (s) Calculate the distance travelled
  4. June 2023, Paper 4, Q19 (5 marks): The graph shows the velocity of a particle over the first 20 minutes of its motion. Velocity Not to scale (m / min) v 0 0 7 15 20 Time (mins) Between 7 minutes
  5. November 2022, Paper 5, Q16 (4 marks): The graph shows the distance travelled by a particle over the first 20 seconds of its motion. 40 35 30 25 Distance 20 (metres) 15 10 5 0 0 5 10 15 20 Time (seco
  6. November 2022, Paper 6, Q12 (6 marks): The graph shows the speed of a car during the first 40 seconds of a journey. 20 15 Speed 10 (m/s) 5 0 0 5 10 15 20 25 30 35 40 Time (s) (a) Write down the accel
  7. June 2022, Paper 5, Q12 (6 marks): An athlete goes for a training run. The graph shows their speed as they run. 4 Not to scale Speed (m/s) 0 400 1000 1200 Time (secs) (a) Write down the athlete’s
  8. November 2020, Paper 4, Q19 (9 marks): (a) The graph shows the speed of a vehicle during the first 40 seconds of motion. 40 35 30 25 Speed 20 (m / s) 15 10 5 0 0 5 10 15 20 25 30 35 40 Time (s) Calcu
  9. November 2019, Paper 4, Q19 (4 marks): The graph shows the distance travelled by a particle over 8 seconds. 12 11 10 9 8 7 Distance (metres) 6 5 4 3 2 1 0 0 1 2 3 4 5 6 7 8 Time (seconds) Estimate th
  10. June 2019, Paper 4, Q14 (7 marks): The graph shows the speed of a train during the first 60 seconds of motion. 25 20 15 Speed (m / s) 10 5 0 0 5 10 15 20 25 30 35 40 45 50 55 60 Time (s) (a) What
  11. November 2018, Paper 6, Q8 (7 marks): The graph shows the speed of a cyclist during 20 seconds of a journey. 14 12 10 8 Speed (m/s) 6 4 2 0 2 4 6 8 10 12 14 16 18 20 Time (s) (a) Find the accelerati
  12. June 2018, Paper 6, Q8 (9 marks): The graph shows the speed of a tram as it travels from the library to the town hall. Speed Not to scale (m/s) 6 0 65 85 Time (s) (a) Calculate the deceleration
  13. November 2017, Paper 5, Q13 (10 marks): The graph shows information about the speed of a vehicle during the final 50 seconds of a journey. At the start of the 50 seconds the speed is k metres per seco
  14. June 2017, Paper 4, Q20 (2 marks): The graph shows the speed, in metres per second, of a particle over the first four seconds of motion. 16 15 14 13 12 11 10 9 Speed (m/s) 8 7 6 5 4 3 2 1 0 0 1 2

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